Exclusion in “Ricardian” Trade

Models

Eduardo Crespo, Ariel Dvoskin and Guido Ianni

Centro Sraffa Working Papers

n. 39

December 2019

ISSN: 2284 -2845

Centro Sraffa working papers

[online]

1

Exclusion in “Ricardian” Trade Models

Eduardo Crespoa, Ariel Dvoskinb, & Guido Iannic

aUFRJ bCONICET-UNSAM

cROMA TRE UNIVERSITY

Abstract

The paper discusses the following result of the so-called ‘Ricardian’ models of interna-

tional trade: the impossibility of exclusion from trade. We show that this result holds due

to the very restrictive assumptions behind these models: (i) commodities are produced by

unassisted labour alone under (ii) complete factor immobility. The moment these assump-

tions are relaxed, the likelihood of exclusion can no longer be neglected. The reason is

the following: even if there were no limits to the fall in the rate of domestic real wages,

production costs would reach a positive lower bound due to the presence of imported

capital goods. Exclusion is therefore the result of this lower bound being higher than the

prevailing international price, for both capital and consumption-goods sectors.

Keywords: Absolute advantage; Comparative advantage; Exclusion from trade; Pattern

of specialization; Ricardian models of trade.

JEL Codes: B27; B51; F11.

1. Introduction1

Since David Ricardo (1951) introduced the notion of comparative advantage (henceforth,

CA) for the first time with the sufficient analytical rigor, the vision has established itself

that differences in productivity across countries do not constitute an unsurmountable ob-

stacle to international trade. Irrespectively of the absolute degree of its technological

backwardness, it is argued, a country will always be able to compensate this deficiency

1 We wish to thank Saverio Fratini, Antonella Palumbo and one anonymous referee for the comments and

suggestions to a previous version of this article. The usual disclaimer applies.

2

with sufficiently low wages. In other words, that there necessarily exists a distributive

configuration that prevents exclusion from trade2.

The claim has been adopted as its own by the neoclassical approach, and formalized

in what are currently known as ‘Ricardian Models of Trade’ (cf. Dornbusch et al, 1977).

Baptized this way precisely because, unlike the other ‘traditional’ class of trade-models

within this approach, which highlight the role played by factor endowments (Heckscher,

1919; Ohlin, 1933; Samuelson, 1948, 1949), the former emphasize – as Ricardo himself

did – the role of productivity differences across countries to explain the pattern of spe-

cialization3. As an expression of their current relevance, most neoclassical trade theorists

recognize that, by themselves, differences in factor endowments do not accurately fit with

the actually observed patterns of trade (cf. Trefler,1995). In what we can safely consider

as one of ‘the’ current graduate textbooks in mainstream international trade theory, we

find Feenstra arguing that:

the Heckscher-Ohlin model is hopelessly inadequate as an explanation for historical or

modern trade patterns unless we allow for technological differences across countries. For

this reason, the Ricardian model is as relevant today as it has always been (Feenstra, 2014,

p. 1)4.

Now, besides the emphasis on countries’ technological differences, the other peculiar-

ity of the neoclassical Ricardian models is that, since they conceive distribution as a

strictly market phenomenon, the required adjustment in distributive variables to avoid

exclusion is automatically triggered every time that, due to its lack of international com-

petitiveness, a country exhibits (at least some) persistent unemployment5,6. And while due

to this reason the neoclassical theory presents itself as the ‘natural environment’, so to

2 In the words of an authoritative scholar in the subject, “A country that is less productive than its trading

partners across the board will be forced to compete on the basis of low wages rather than superior produc-

tivity. But it will not suffer catastrophe, and indeed will normally still benefit from international

trade”(Krugman, 1991, p. 812). 3 To avoid any misunderstandings, it is worth noting that the term ‘Ricardian models’ is actually mislead-

ing. Indeed, beyond the mentioned similarity between these models and Ricardo’s own contribution, there

are irreconcilable differences between the two. In particular, while in the latter distribution is determined

by non-economic factors, in the former the real wage necessarily adjusts to ensure both internal (i.e. full-

employment) and external (i.e. balance of payments) equilibria. (For a detailed analysis of Ricardo’s own

contribution to trade theory, see Gehrke (2015). 4 As Gandolfo (2014) notes, among the causes that explain the different levels of productivity across

countries, technological differences need not be considered in the strictest engineering sense. Recent liter-

ature has additionally emphasized the role of institutions and even cultural traits as causes of CA (see, e.g.

Belloc and Bowles, 2013). 5 “The reason that it is still possible for the home country [the country that has absolute disadvantages in

all commodities] to export”, explains Feenstra, “is that its wages will adjust to reflect its productivities:

under free trade, its wages are lower than those abroad” (Feenstra, 2014, p. 3, Emphasis added). 6 Even those models that, by emphasizing the importance of increasing returns to scale – what is currently

known as ‘New Trade Theory’ – seem to be able to do without CA as an explanation of trade – need that

distributive variables adjust to compensate potential differences in productivity caused, for instance, by

countries’ significantly different sizes (cf. Krugman, 1980, p. 958). This helps understanding why the pro-

ponents of New Trade Theory still accept the validity of CA (see Krugman, 1991).

3

speak, to develop these models, the fact is that they can also be complemented, in princi-

ple, by an alternative theory of prices and distribution. Little wonder then that, scholars

that do not necessarily adhere to this approach to value and distribution, nonetheless have

explicit recourse to the Ricardian models (cf. e.g. Cimoli and Porcile, 2010; Razmi, 2012)

or at least to the general message they transmit (cf. e.g. Frenkel and Ros, 2006; Bresser-

Pereira, 20087), to justify why the fall in real wages can contribute to diversify the pro-

ductive structure of a particular nation, by allowing the addition of new sectors that were

not profitable at a higher real wage. The difference with respect to the marginalist models

being that the fall in real wages is, in this case, conceived as the outcome of deliberate

economic policy (e.g. a real devaluation).

The plurality of schools that continue to rely on Ricardian models, strongly suggests

that their critical examination is relevant even beyond their implications for the neoclas-

sical theory of international trade. In this respect, it is true that a group of authors, on the

basis of the revival of the classical approach after Sraffa’s (1960) seminal contribution,

has convincingly argued against the spontaneous adjustment in income distribution

through the action of the supply-and-demand forces, either because distribution is ‘exog-

enous’ to the market (cf. Brewer, 1985; Gibson, 1981; Shaikh, 1980; Parrinello, 1979,

2010), or because the forces of supply and demand may not work in the ‘right’ direction

(Metcalfe and Steedman, 1972; Steedman and Metcalfe, 1977). However, these objec-

tions alone do not exclude the possibility that, if the change in distribution were the out-

come of economic policy, specialization might actually take place.

In this work we critically face this issue. And we show that, independently of its cause

(either unemployment, as it is argued by the marginal approach, or the outcome of delib-

erate economic policy, as some non-orthodox scholars suggest), the fall in the real wage

may not be able to compensate productivity differences and avoid the exclusion from

trade; even if, for the sake of argument, we allow wages to fall to arbitrarily low levels,

even zero.

Within what we can identify as the canonical Ricardian model of trade (cf. Matsu-

yama, 2008), exclusion is not possible essentially because production is assumed to re-

quire unassisted labour alone. Therefore, conveniently enough, when wages fall, produc-

tion costs can be arbitrarily reduced relative to the rest of the world, and compensate any

possible technological backwardness. But this outcome ceases to hold the moment that,

realistically enough, we consider that production employs capital goods and, moreover,

we also allow for – thanks to the mobility of capital across countries (hypothesis not less

realistic, given the actual conditions of global production) – at least some tendency to

equalization of profit rates across countries. We argue therefore, that, under these two

premises – production with capital goods and free capital mobility–, exclusion from trade

can indeed happen. We therefore develop an argument firstly presented in Parrinello

(2010, Section 4, p. 55), where the possibility of exclusion is considered, but not suffi-

ciently explored in its causes as the issue deserves.

7 For a critical assessment to Frenkel and Ros’s (2006) contribution, and more generally, to what is cur-

rently known as the ‘New structural approach’, see Dvoskin et al. (2019); for a critical reconstruction of

Bresser’s contribution, see Dvoskin and Feldman (2018).

4

The argument to be developed in the article can be summarized by the following three

propositions: (a) the moment production requires, besides labour, the employment of im-

ported capital goods, there is a lower bound to the fall in production costs, even if domes-

tic wages fall to zero; (b) when the available technology is sufficiently backward, it may

well happen that this lower bound is higher than the corresponding international price;

and finally, (c) the impossibility to domestically produce these capital goods is the result

of the international profit rate being higher than the maximum rate affordable by its do-

mestic production.

The thread of the argument is developed as follows. In Section 2 we present the no-

trade-exclusion condition, both for the 2 and the 𝑁 consumption-goods cases, under the

standard assumptions of Ricardian models; specifically, that commodities are produced

by unassisted labour alone that is paid at the end of the production cycle. In Section 3, we

partially relax these assumptions: we allow for the existence of capital, although it con-

sists entirely of anticipated wages. We show that in this case, capital mobility is not

enough for exclusion, but it may happen that a country is excluded from trade if labour is

the mobile factor. And while this is a rather implausible assumption, this ‘laboratory’ ex-

ample will be useful to grasp why, when production costs cannot be arbitrarily reduced,

trade-exclusion becomes a possibility. Section 4 finally considers the truly relevant case

of production of capital goods under capital mobility, where the main result of the paper

is shown, both for 2 and 𝑁 consumption goods. The article concludes in Section 5 with a

brief summary of the argument and some implications of our results.

2. Comparative advantage in canonical Ricardian trade models

2.1. Two commodities

To settle the grounds of the discussion, it is enough to consider the production side of a

canonical Ricardian model of two countries 𝑖 = {𝐴; 𝐵} that produce two different con-

sumption goods 𝑧 = {0; 1}, by unassisted labour alone under constant returns to scale.

We further keep the standard assumptions of these models of labour immobility across

countries and one common currency to abstract from exchange-rate considerations.

If 𝑙𝑧𝑖 and 𝑤𝑖 stand, respectively, for the unitary labour requirement of commodity 𝑧 and

for the level of money wages in country 𝑖 = 𝐴, 𝐵 in terms of the common monetary unit;

then, the money cost of production of 𝑧 in 𝑖 is determined by:

𝑐𝑧𝑖 = 𝑤𝑖𝑙𝑧

𝑖 [1]

Notice from [1] that costs of production can be arbitrarily reduced with appropriate

reductions in the wage rate. In other words, 𝑐𝑧𝑖 goes to zero when 𝑤𝑖 goes to zero.

Under international trade, due to the action of competition, commodity 𝑧 will be pro-

duced in the country that can supply it at the minimum average costs, 𝑐𝑧𝑖 . Therefore 𝑝𝑧,

the price of commodity 𝑧, is:

𝑝𝑧 = 𝑚𝑖𝑛{𝑐𝑧𝐴; 𝑐𝑧

𝐵} [2]

5

2.2. Impossibility of exclusion from trade

We can proceed to examine why exclusion from trade is not possible. To see this, let us

follow the standard procedure (see Dornbusch et al. 1977, Section 2, Gandolfo, 2014,

Section, 2.4.2), and define the relative wage between the two countries, 𝜔 ≡ 𝑤𝐴/𝑤𝐵.

Suppose now that country A has absolute cost disadvantages in the production of both

commodities (𝑐𝑧𝐵 < 𝑐𝑧

𝐴 ⇒ 𝑝𝑧 = 𝑐𝑧𝐵∀𝑧). Consider next a notional decrease in 𝑤𝐴, and

therefore, in the relative wage 𝜔. Since the cost of production of 𝑧 in country A can be

arbitrarily reduced by reductions in its own wage rate, this will eventually ensure that the

condition 𝑐𝑧𝐴 < 𝑐𝑧

𝐵 will hold for at least one 𝑧. As a result, country A will not be excluded

from trade.

It is convenient to notice that as long as the productive structure does not change, the

fall in 𝜔 necessarily implies that real wages in country 𝐴 are falling in terms of any com-

modity. Since all commodities are being produced in country 𝐵, prices are proportional

to 𝑤𝐵 and, hence, 𝑤𝐴/𝑝𝑧falls, for all 𝑧. The moment a particular commodity 𝑧 starts

being produced in country 𝐴, the fall in 𝑤𝐴 causes the money price of this commodity to

fall proportionally8, hence the real wage no longer falls in terms of this particular com-

modity, but it will continue decreasing in terms of any imported commodity. Likewise, in

the case that all commodities are being produced in country 𝐴, a fall in 𝜔 will only rise

the real wage in country 𝐵, leaving real wages in country 𝐴 unaffected. Consequently, a

change in 𝜔 is tantamount to a change in the real wage either in country A or in country

B, in terms of any commodity that is not being produced by this country 9. Therefore, as

it is usual in the literature, to examine the pattern of trade, for analytical convenience we

will here consider variations in the relative wage, always having in mind that these vari-

ations imply changes in real wages.

2.3. The pattern of specialization

One can then proceed to determine the precise interval of 𝜔 that allows specialization in

production. To do this, consider first the comparative cost of the same commodity in

countries A and B, 𝑐𝑐𝑧:

𝑐𝑐𝑧 =𝑐𝑧𝐴

𝑐𝑧𝐵=𝑤𝐴

𝑤𝐵

𝑙𝑧𝐴

𝑙𝑧𝐵= 𝜔

𝑙𝑧𝐴

𝑙𝑧𝐵 [3]

The value of 𝜔 that would be necessary to equalize production costs of commodity

𝑧in both countries (𝑐𝑐𝑧 = 1), is given by:

8 As we will see in Section 4 below, when production includes imported capital goods, since money prices

are no longer proportional to money wages, a fall in 𝑤𝐴 will also cause a fall in the real wage even in terms

of those commodities that are being produced in country A, provided that these commodities use, either

directly or indirectly, imported commodities. 9 As can be inferred from the previous note, with imported capital goods the fall in 𝜔 will also cause a

fall in real wages in country A (and a rise in country B) even in terms of any commodity, provided that it

employs imported inputs.

6

𝐿(𝑧) =𝑙𝑧𝐵

𝑙𝑧𝐴 [4]

Function 𝐿(𝑧), which has been extensively used in the literature (see for instance Dorn-

busch et al., 1977, and more recently, Matsuyama, 2008 and Razmi, 2012), presents how-

ever two important properties that are not always sufficiently stressed: (𝑖) it depends on

technical coefficients alone, and (𝑖𝑖) it can be determined independently from other pro-

duction methods besides the one(s) employed in the production of commodity 𝑧. We will

come to these properties in the following sections.

The comparison between the actual value of 𝜔 and the value of 𝐿(𝑧) allows determin-

ing whether commodity 𝑧 can be (profitably) produced in country A. In particular, 𝑐𝑧𝐴 ≤

𝑐𝑧𝐵 requires that:

𝜔 ≤ 𝐿(𝑧) [5]

Without loss of generality, the two commodities can always be numbered so that 𝐿(𝑧)

is decreasing in 𝑧, namely that 𝐿(1) < 𝐿(0). And this means that whenever 𝐿(0) < 𝜔

both commodities are produced only in country B, while when 𝜔 < 𝐿(1) both commod-

ities are produced only in country A. Finally, there is (full) specialization (A produces

commodity 0 and B produces 1)10, if the relative wage falls within the following interval:

0 < 𝐿(1) ≤ 𝜔 ≤ 𝐿(0) [6]

In Figure 1 we represent the shape of function 𝐿(𝑧) for the simple two-commodity case.

Figure 1- The pattern of specialization in the two-commodity case.

Of the three possible cases depicted in Figure 1, sufficient flexibility in the relative

wage ensures that condition [6] will eventually hold and therefore specialization will pre-

vail.

10 Notice that the opposite pattern of specialization is not possible since it would simultaneously require

that 𝜔 ≤ 𝐿(1) and 𝜔 ≥ 𝐿(0), which cannot happen since, by assumption, 𝐿(0) > 𝐿(1).

𝜔

𝑧 1 0

𝐿(0)

𝐿(1)

B produces both commodities

A produces commodity 0 and B commodity 1

A produces both commodities

7

2.4.Many commodities

The extension of the previous result to the production of many (N) commodities is rather

straightforward. Provided that all goods are produced by unassisted labour alone, it is still

possible to order commodities such that:

0 < 𝐿(𝑁 − 1) ≤ 𝐿(𝑁 − 2) ≤ ⋯ ≤ 𝐿(0) [7]

Then, for the existence of specialization – partial, in this case –, it is enough that the

relative wage, 𝜔, falls in the following interval:

0 < 𝐿(𝑁 − 1) ≤ 𝜔 ≤ 𝐿(0) [8]

Condition [8] therefore excludes a situation in which all commodities are only

produced in one country [either in country B, when 𝜔 > 𝐿(0), or in country A, if 𝜔 <

𝐿(𝑁 − 1)]. Condition [8] will hold if relative wages are determined by market forces but

it may also be the outcome of deliberate public policy. Hence, commodity 0 will be

produced by country A and commodity 𝑁 − 1 by country B, while the location of

production of the remaining commodities 1,… ,𝑁 − 2, can be ascertained by condition

[5], once the precise level of 𝜔 is determined11. In Figure 2, a possible pattern of trade is

represented when𝜔 = �̅�.

Figure 2- The pattern of trade with many commodities.

The figure shows that for the given relative wage �̅�, country A produces commodities

0,1... up to 𝑧̅ , while the remaining commodities are produced by B.

11 The determination of this level of 𝜔 is beyond the scope of this article. If, for instance, one develops

the argument internally to the neoclassical approach, it will generally depend, besides technology, on the

other data of neoclassical theory – the preference structure of consumers and labour endowments (on this

point see e.g. Dornbusch et al, 1977). But, as argued in the introduction, nothing prevents us from assuming

that the precise level of 𝜔 is the outcome of public policy, as in Razmi (2012).

𝜔

𝑧 0 1 2 𝑁 − 1 𝑁 − 2 𝑁 − 3 𝑧̅ 𝑧̅ + 1

𝐿(0)

𝐿(1)

𝐿(2)

𝐿(𝑧̅) �̅�

𝐿(𝑧̅ +

1)𝐿(𝑁 −

3)𝐿(𝑁 − 2) 𝐿(𝑁 −

1)

𝑧̅ − 1

𝐿(𝑧̅ − 1)

8

3. Capital as anticipated wages

In this section we reconsider the possibility of exclusion from trade when capital consists

entirely in anticipated wages. We continue assuming that there are 𝑁 consumption goods,

still produced by unassisted labour alone. However, since wages are paid at the beginning

of the production cycle, a positive rate of profits is included in normal production costs.

The cost of production of a generic commodity 𝑧 in country 𝑖 is now determined by:

𝑐𝑧𝑖 = 𝑤𝑖𝑙𝑧

𝑖 (1 + 𝑟𝑖) [9]

where 𝑟𝑖 is the rate of profits earned in country 𝑖. As before, due to the action of com-

petition, under international trade the price of 𝑧 will be determined by condition [2]:

𝑝𝑧𝑖 = 𝑚𝑖𝑛{𝑐𝑧

𝐴; 𝑐𝑧𝐵} [2]

And, therefore, commodity 𝑧 can be simultaneously produced by the two countries only

when 𝑐𝑐𝑧 = 1, that is:

𝑤𝐴𝑙𝑧𝐴(1 + 𝑟𝐴) = 𝑤𝐵𝑙𝑧

𝐵(1 + 𝑟𝐵) [10]

Let us define the relative (gross) profit rate, ≡1+𝑟𝐴

1+𝑟𝐵 . Condition [10] can be expressed

in terms of a modified 𝐿 function, which we will call 𝑇. This function takes the following

form:

𝜔 = 𝑇(𝑧, 𝜌) =𝐿(𝑧)

𝜌 [11]

Like 𝐿(𝑧) in the previous section, 𝑇(𝑧, 𝜌) gives the relative wage that allows commod-

ity 𝑧 to be produced by the two countries at the same costs (the difference being that,

differently from 𝐿(. ), 𝑇(. ) also depends on income distribution; see the next paragraph).

This means that when 𝜔 < 𝑇(𝑧, 𝜌) commodity 𝑧 is produced only in country A, while it

is produced only in country B when 𝜔 > 𝑇(𝑧, 𝜌). Therefore, the prevailing pattern of

trade is again simultaneously determined with income distribution. Consequently, country

A will produce and export all commodities 𝑧 satisfying 𝜔 ≤ 𝑇(𝑧, 𝜌).

We can now proceed to examine the condition that ensures the existence of trade and

the possibility of specialization. This can be done by applying the same logic as before.

Although, now, the relative wage that equalizes costs does depend on the relative profit

rate, 𝜌 – 𝑇(. ) does not inherit property (𝑖𝑖) from 𝐿(. ) (see Section 2.3) – the difference

between functions 𝐿(.) and 𝑇(. ) is more apparent than real: from [11] it is immediate that

𝜌 only rescales function 𝐿(𝑧) without affecting its original shape12. Then, 𝐿(𝑁 − 1) ≤

⋯ ≤ 𝐿(0) implies 𝑇(N − 1; 𝜌) ≤ ⋯ ≤ 𝑇(0, 𝜌) for any feasible level of 𝜌. Furthermore,

for feasible values of 𝜌(> 0), 𝐿(. ) > 0 implies 𝑇(. ) > 0. In words, the ranking of com-

modities in terms of comparative costs is preserved and the relative wage that prevents

exclusion from trade is necessarily positive.

With these remarks, the no-exclusion-from-trade condition can be written as:

12 In the following section we will see that when there is production of capital goods, the absence of this

property does become relevant for exclusion.

9

0 < 𝑇(𝑁 − 1; 𝜌) ≤ 𝜔 ≤ 𝑇(0, 𝜌) [12]

which due to [11] can be expressed as:

𝐿(𝑁 − 1)

𝜌≤ 𝜔 ≤

𝐿(0)

𝜌 [12’]

Or alternatively, as:

𝐿(𝑁 − 1) ≤ 𝜌𝜔 ≤ 𝐿(0) [13]

3.1. Factor mobility

So far, we have presented function 𝑇(𝑧, 𝜌) in its general form, namely neglecting the

possibility of ‘factor’ mobility across countries. When capital is internationally mobile,

then profit rates are equalized across countries and the following condition must hold:

𝜌 = 1 [14]13

Notice that, when [14] is duly considered, [13] boils down to [8] (the no-exclusion-

condition when there was no capital). And we already know that if the relative wage is

flexible enough, [13] will eventually hold, and therefore there will be specialization under

conditions of trade.

To see why the consideration of capital as anticipated wages poses no particular diffi-

culties when there is capital mobility and labour immobility across countries, it is useful

to consider the opposite, although empirically implausible, situation of full labour mobil-

ity (𝜔 = 1) and capital immobility (𝜌 ≠ 1, in general). Under these conditions, the no-

trade-exclusion condition [13] becomes:

𝐿(𝑁 − 1) ≤ 𝜌 ≤ 𝐿(0) [15]

And the fact is that [15] may not hold because, when, for instance, 𝐿(0) < 𝜌 and there-

fore country A happens to be excluded from trade, the necessary fall in 𝜌 to ensure spe-

cialization may require a negative net profit rate in country A. To see this, we have re-

course to Figure 3, which illustrates the argument in graphical terms.

13 The moment the mobility of capital is considered, one could wonder why differences in production

methods across countries still prevail. This is due both to technical and institutional reasons. As to the

former, some methods of production employ specific kinds of labour – well trained engineers, for instance

– that may not be available in some countries. Moreover, due to economies of agglomeration, indivisibilities

and even irreversibilities that arise in production, but also due to differences in infrastructure, some coun-

tries may not be able to employ the most ‘advanced’ methods of production, independently of the price

system. Regarding the institutional reasons, as argued in Parrinello (2010), methods of production also

reflect the different functions performed by the National Government. Different national institutions, which

include public organizations, the rule of law but also informal social norms, may constrain the choice of

available techniques, even when capital is freely mobile, and technical knowledge is evenly diffused.

10

Figure 3 - 𝑇(𝑍, 𝜌) = 𝜔 in the 𝜌 − 𝜔 space.

Condition [13] is represented in the figure by the grey area within the solid black curves.

Its upper limit represents the different 𝜌 − 𝜔 configurations that allow commodity 0 to

be produced in both countries, while its lower limit shows the same thing for commodity

𝑁 − 1. Note that, due to [11], for any level of 𝜌, 𝑇(𝑁 − 1, 𝜌) is always below 𝑇(0, 𝜌) in

the 𝜌 − 𝜔 space. In turn, the dashed curve in the figure illustrates the possible distributive

configurations that would allow a specific commodity 𝑧̅ to be produced by the two coun-

tries at the same costs. The dashed curve therefore supports a specific pattern of trade:

country A specializes in the production of all 𝑧 ∈ [0; 𝑧̅] and B in the production of 𝑧 ∈[𝑧̅; 𝑁 − 1]14. This is because it also follows from [11] that all the possible 𝑇(𝑧, 𝜌) curves

(one for each 𝑧) do not intersect each other, the curves 𝑇(𝑧, 𝜌) being always above 𝑇(𝑧 +

1; 𝜌) for any 𝜌. Hence if 𝑧 is produced in country A, 𝑧 − 1 will be produced in this coun-

try, too.

We know that country A will be excluded from trade if 𝜔 > 𝑇(0, 𝜌) – namely when

𝜔𝜌 > 𝐿(0)– like in point 𝐸 = (1; 1) in the figure, which lays strictly above the grey

area. Notice that point 𝐸 also illustrates the distributive configuration when both labour

and capital are fully mobile, and thus shows that in this case exclusion is possible. A

necessary and sufficient condition for this result to hold is that 𝐿(𝑧) < 1 for all 𝑧. This

case is rather trivial since, being all factors mobile, it limits itself to replicate the results

of a closed economy, where, as is well known, competition does exclude the choice of

technologically backward methods of production.

We now move to the truly interesting cases for international trade, in which at least

one factor is not mobile. With capital mobility, 𝜌 is the sole distributive variable that is

constrained to be equal to unity. The figure shows that, for 𝜌 = 1, an economically rele-

vant (non-negative) level of 𝜔 that prevents exclusion (i.e. 𝜔 ∈ [𝐿(𝑁 − 1); 𝐿(0)] in the

14 Of course, with a finite number of commodities, only by fluke the actual distributive configuration will

exactly verify 𝜔 = 𝑇(𝑧̅; 𝜌). So, generally, 𝑧̅ will be produced only in one country.

𝜔

𝜌

𝑇(0; 𝜌)

𝑇(𝑁 − 1; 𝜌) 𝑇(𝑧̅; 𝜌)

1

1

�̅� (1 + �̅�𝐵)−1

𝐿(0)

𝐿(𝑁 − 1)

𝑬

11

figure) always exists. Although now there is capital in production, exclusion is still not

possible because, as capital consists entirely in anticipated wages, any level of the profit

rate that could be imposed within a country by capital mobility, would still be realized if

wages were appropriately reduced.

On the contrary, the figure shows that when labour is the mobile factor (𝜔 = 1), the

necessary level of 𝜌 that would prevent exclusion of country A, �̅�, may not be economi-

cally meaningful, since it may require a negative profit rate in this country. To see this,

notice that, differently from 𝜔 – which tends to zero when 𝑤𝐴 goes to zero –, 𝜌 does not

approach zero when 𝑟𝐴 does. Recalling that 𝜌 ≡1+𝑟𝐴

1+𝑟𝐵, it is immediate that this variable

could be reduced, either because of a higher 𝑟𝐵 or of a lower 𝑟𝐴. Now, let us assume that

all commodities are being produced in country B with a rate of profits equal to �̅�𝐵 (country

A is being excluded from trade). It follows that there exists a lower bound to 𝜌, which

corresponds to 𝑟𝐴 = 0 and 𝑟𝐵 = �̅�𝐵. And, as it is shown in the figure, since �̅� <

(1 + �̅�𝐵)−1, country A cannot avoid its exclusion from trade. Or, in other words, the only

way the threshold, �̅�, can be achieved is by allowing 𝑟𝐴 to be negative15.

To conclude with this section, we could alternatively grasp the different implications

of capital and labour mobilities, by inspecting the cost equation of commodity 𝑧– 𝑐𝑧𝑖 =

𝑤𝑖𝑙𝑧𝑖 (1 + 𝑟𝑖) – and considering whether this cost in country A could be reduced below

the respective cost in country B, 𝑐𝑧𝐵. As it can be seen, regardless how small 𝑐𝑧

𝐵 is, when

capital is the mobile factor, the cost of production of 𝑧 in country 𝐴 would eventually tend

to zero if wages were sufficiently reduced in this country, therefore overcoming producers

in country B.

On the contrary, with labour mobility, even if 𝑟𝐴 were reduced to zero, production

costs would remain positive and– since 𝑤𝐴 = 𝑤𝐵 = 𝑤 – they could not be further re-

duced below 𝑤𝑙𝑧𝐴. In other words, labour mobility imposes a lower bound to production

costs that may prevent competitiveness in every commodity.

4. Production with capital goods

In this section, we extend the analysis further and incorporate capital goods. As we have

shown in the previous section, the possibility of trade-exclusion was the consequence of

the existence of a positive lower bound in production costs. But with capital as anticipated

15 That 𝑟𝐴 cannot fall below zero is obvious enough to need justification. However, the reader may still

wonder whether there are forces that would increase �̅�𝐵 sufficiently to promote the competiveness in coun-

try A. If, on the one hand, one develops the argument internally to the neoclassical theory,�̅�𝐵 is the rate of

profit corresponding to the world endowment of labour being employed in country B (this due to the neo-

classical full-employment condition coupled with the assumption of labour-mobility). Given the preference

structure of consumers and technology, under these conditions capital in country B is as scarce as possible,

and therefore its rate of remuneration is maximized at �̅�𝐵, and hence it cannot be further increased. If, on

the other hand, we consider an alternative, ‘non-mechanical’ theory of distribution, the forces that determine

the rate of profits may be so complex that there is simply no reason to expect a further increase in �̅�𝐵, much

less as the outcome of an economic policy adopted in country A, aiming to promote its own competitive-

ness.

12

wages this could only happen when labour was the mobile factor, which was of course

not a very realistic assumption. The aim of the present section is to show that under a

more plausible framework of production with capital goods, the mobility of capital (or at

least some mobility) can also give raise to such a lower bound.

4.1. Production with capital goods: two commodities

To that end, consider a simple economy that produces two commodities. We suppose that

commodity 1 is a circulating capital good, while commodity 0 is a pure consumption

good. The cost of production of a generic commodity 𝑧 in country 𝑖, is now given by:

𝑐𝑧𝑖 = (𝑤𝑖𝑙𝑧

𝑖 + 𝑎1𝑧𝑖 𝑝1)(1 + 𝑟) [16]

where 𝑎1𝑧𝑖 is the unitary requirement of commodity 1 in the production of commodity 𝑧

and 𝑟 is the international profit rate under the assumption of capital mobility; while 𝑝1 =

min{𝑐1𝐴; 𝑐1

𝐵} is the normal price of the capital good employed in production (on this see

immediately below).

4.1.1. Function 𝑇 with capital goods

So far, the conditions that ensured the existence of trade were determined with the help

of function 𝑇. The presence of capital goods entails, however, the following difficulty:

since costs of production now depend on the price of the capital good employed, function

𝑇 will vary with the location of production of the capital good. To see this, consider the

comparative cost of the generic commodity 𝑧, which, recall, is the basis to derive function

𝑇:

𝑐𝑐𝑧 =𝑤𝐴𝑙𝑧

𝐴 + 𝑎1𝑧𝐴 𝑝1

𝑤𝐵𝑙𝑧𝐵 + 𝑎1𝑧𝐵 𝑝1

[17]

with 𝑝1 given by:

𝑝1 =(1 + 𝑟)𝑙1

𝐴

1 − 𝑎11𝐴 (1 + 𝑟)

𝑤𝐴 [18]

if 𝑐1𝐴 < 𝑐1

𝐵. Or by:

𝑝1 =(1 + 𝑟)𝑙1

𝐵

1 − 𝑎11𝐵 (1 + 𝑟)

𝑤𝐵 [18’]

when 𝑐1𝐴 ≥ 𝑐1

𝐵.

If, for the sake of argument, [18’] holds, the value of function 𝑇 for the consumption

good 0 – that, recall, gives the relative wage, 𝜔, that renders 𝑐𝑐0 = 1– would be given

by:

𝑇(0, 𝑟) = 𝐿(0) + (𝑎10𝐵 − 𝑎10

𝐴 )𝑙1𝐵

𝑙0𝐴 [

1 + 𝑟

1 − 𝑎11𝐵 (1 + 𝑟)

] [19]

13

It is readily seen that function 𝑇(0, 𝑟) in [19] does not inherit any of properties (𝑖) and

(𝑖𝑖) of function 𝐿(𝑧) derived when labour was the only input (see Section 2.2)16: neither

the value of the function for commodity 0 is independent of income distribution (it de-

pends on the level of 𝑟) nor is independent from the conditions of production of the other

industries (it depends on the technical coefficients of the capital-good sector)17. The im-

plications for the possibility of trade exclusion are discussed in the following subsection.

4.1.2. Exclusion in the production of the consumption good

We now proceed to examine the possibility of trade-exclusion. Since our aim is mainly

negative, the argument is developed in the following way. First, we assume that condition

[18’] holds – i.e. the capital good is produced in country B because 𝑐1𝐴 > 𝑐1

𝐵– and identify

a sufficient condition that ensures that the consumption good 0 can only be produced in

country B. And then, in Section 4.1.3 we will identify a second sufficient condition that

ensures that the capital good can only be produced in country B too, therefore justifying

the recourse to condition [18’] in the first step.

Let us start with the first step. From [19], we know that country A will not be able to

produce good 0 if the actual relative wage, 𝜔, is higher than the level that allows produc-

tion costs to be equalized across countries, given by 𝑇(0, 𝑟). Namely, when:

𝑇(0, 𝑟) < 𝜔 [20]

In order to ensure exclusion, condition [20] must hold for any economically feasible

value of the relative wage. This will be immediately ensured if the required relative wage

is negative:

𝑇(0, 𝑟) < 0 [21]

as 𝜔 ≥ 0 would immediately imply [20] holds. We will thus show that this possibility

cannot be excluded a priori. To see it, notice that, differently from 𝐿(𝑧) in the canonical

Ricardian model, function 𝑇(0, 𝑟) has one additional term (compare [19] to [4]). This

term is the analytical expression of the absence of property (𝑖𝑖) – the influence on 𝑇(. )

of production methods of other industries – when there are capital goods. And its rele-

vance is evident the moment one notices that its sign depends on the sign of (𝑎10𝐵 − 𝑎10

𝐴 ).

While the importance of the absence of property (𝑖) – the influence on 𝑇 of income dis-

tribution – is that the absolute magnitude of this term increases with the level of the profit

rate18.

Therefore, if productivity of the consumption-good sector in country A is sufficiently

low, 𝑎10𝐴 is high enough, condition [21] may hold, therefore implying that the necessary

16 Of course, that none of this two properties hold is independent of the fact that the capital good is

produced in countries A or B. 17 Under the very simple conditions of production assumed in this section, property (ii) still holds for the

capital-good sector. Nevertheless, it would immediately cease to hold the moment more than two basic

goods were used in production. 18 Actually, a further implication of the absence of properties (i) and (ii) is that the shape of function 𝑇

will change when income distribution changes. The deep consequences of this on the theory of comparative

advantages cannot be examined here. We hope to do this in a future contribution.

14

level of the relative wage that would equalize production costs across countries is nega-

tive, which has of course no sense from an economic point of view.

An alternative, perhaps more intuitive, way to present the argument can be directly

derived from [17] and considering whether 𝑐𝑐0 > 1 holds. That is:

(𝑎10𝐴 − 𝑎10

𝐵 )𝑝1 > 𝑤𝐵𝑙0𝐵 − 𝑤𝐴𝑙0

𝐴 [22]

[22] shows that even if country A has lower wage-costs than B (the right-hand side is

positive), it will have absolute cost disadvantages in the production of the consumption

good (and therefore, provided 𝑐1𝐵 < 𝑐1

𝐴, in the production of the two commodities) when

its ‘capital-goods’ costs relative to B, are ‘sufficiently large’ (the left hand side is positive

and greater than the right hand side). And the fact is that this may happen even when the

wage rate in country A goes to zero. In this case, country A may be unable to compensate

with low wages its relative ‘backwardness’ in the employment of the capital good in the

consumption-good industry19.

Finally, the reason behind exclusion could also be grasped from a third angle that em-

phasizes the role of production costs in trade. As we already know, exclusion is caused

by the existence of a lower bound in production costs. And this lower bound arises when

there are capital goods because producers of the consumption good in country A find it

convenient to import the capital good from country B, since it is more cheaply produced

there. If this is the case, from [16] and [18’], the price (cost of production) of the con-

sumption good in country A is given by:

19 At first sight, exclusion in the production of some sector for any level of the real wage due to techno-

logical backwardness may seem too strong a result to hold in reality; however, a quick inspection on his-

torical literature on the subject indicates that huge and increasing – productivity differences across countries

have emerged since the Industrial Revolution, thus giving substantial plausibility to our theoretical claims.

Two examples will suffice to strengthen our argument from an historical perspective. If before 1820 the

differences in income levels – measured in purchasing power parity – by country between the richest re-

gions of the world, such as England, Holland, or the lower Yangtze River Valley, compared to some regions

of Africa or Central Asia did not exceed the proportion of 3 to 1, 150 years later these differences rose to

more than 60 (cf. Bairoch et al.,1981; Maddison, 2003). Indeed, Williamson (2011, chapter, 5) documents

that it is after the revolution of transport caused by railroads and steamboats – that is, when transcontinental

trade acquired gigantic proportions and started to include subsistence (or basic) goods among merchandised

commodities – that the jump in European productivity levels and the fall in transport costs led to a change

in the terms of trade that drastically reduced the price of industrial products; this literally destroyed manu-

factures in the rest of the planet, especially in the most advanced areas of Asia. Hardly any distributive

change could have reversed this trend in productivity levels per worker, which in the course of few decades

went from a ratio 1:1 to 20:1, as it happened, for example, with textiles produced in Manchester and Bengal.

Mazoyer and Roudart (2006) further document that, decades later, something similar happened when agri-

culture also began to industrialize with the introduction of machinery – e.g. tractors – and increasing inputs

from the chemical industry – e.g. fertilizers, herbicides, fungicides – were introduced. Simultaneously, re-

gions with abundant endowments of fertile lands of temperate or subtropical climate such as the US Mid-

west, Canada, Australia, New Zealand, Argentina and Uruguay were inserted into the world market by the

new transports. These changes modified the terms of exchange of agricultural production throughout the

planet making production for the market of peasants who worked with reduced levels of productivity in

large regions of Latin America, Asia, Africa and even Europe, unfeasible. Of course, these are just two

examples, but in any case they strongly suggest the divergent trends in countries productivities that have

emerged in the last 200 years.

15

𝑐0𝐴 = (1 + 𝑟) (𝑙0

𝐴𝑤𝐴 + 𝑎10𝐴

(1 + 𝑟)𝑙1𝐵𝑤𝐵

1 − 𝑎11𝐵 (1 + 𝑟)

) [23]

which has the implication that 𝑐0𝐴 > 0 even when 𝑤𝐴 = 0. In other words, since the cap-

ital good is imported form B, production costs do not go to zero even if 𝑤𝐴 would fall

arbitrarily close to zero.

4.1.3. Exclusion in the production of the capital good

Let us now move to the second step and justify that recourse to [18’] in the previous

subsection (the condition that shows that the capital good is produced in country B). For

this, notice that, since 𝑎11𝑖 > 0, there is a maximum rate of profits that the capital-good

sector in each country can afford, 𝑅𝑖. This is the rate that would be obtained from [16]

(with 𝑧 = 1) if wages were zero in country 𝑖:

𝑅𝑖 =1 − 𝑎11

𝑖

𝑎11𝑖

[24]

Suppose then, without loss of generality, that 𝑎11𝐵 <𝑎11

𝐴 . It follows that 𝑅𝐴 < 𝑅𝐵. It can

be shown that, if the international profit rate belongs to the following interval:

𝑅𝐴 < 𝑟 < 𝑅𝐵 [25]

then, the capital good will be produced in country B at lower costs than in country A for

any feasible (non-negative) level of wages in the latter. (Actually, the profit rate need not

be necessarily uniform across countries for the argument to hold. It is enough that, due

the existence of some mobility of capital, the profit rate in country A bears some relation-

ship with the one obtained in country B, provided that 𝑟𝐴satisfies [25]).

In fact, when the level of the international profit rate, 𝑟, is higher than the maximum

level affordable by the capital good-sector in country A, 𝑅𝐴, then it follows from [24] that

(1 + 𝑟)𝑎11𝐴 > 1. And this means that the capital-good sector in this country would not

reach international competitiveness, even when 𝑤𝐴 = 0. Formally, [16] (with 𝑧 = 1 and

𝑖 = 𝐴) and [25] both imply:

𝑐1𝐴 = (1 + 𝑟)𝑤𝐴𝑙1

𝐴 + (1 + 𝑟)𝑎11𝐴 𝑝1 > (1 + 𝑟)𝑤𝐴𝑙1

𝐴 + 𝑝1 ≥ 𝑝1 [26]

where the equality follows from [16], the strict inequality from (1 + 𝑟)𝑎11𝐴 > 1 and the

weak inequality from 𝑤𝐴 ≥ 0. Hence, 𝑐1𝐴 > 𝑝1 even if 𝑤𝐴 = 0. And therefore [18’] is

justified20.

If we further recall that condition [21] shows that this country may be also unable to

compensate with low wages its backwardness in the employment of the capital good, the

joint result is that, even if full wage flexibility allows real wages to drop to zero, country

A may be excluded from trade. A numerical example is provided in Appendix A.

20 Since 𝑟 < 𝑅𝐵 and 𝑤𝐵 > 0 then: 𝑝1 = min{𝑐1

𝐴; 𝑐1𝐵} = 𝑐1

𝐵 and [18’] holds.

16

4.2. Many consumption goods

The extension of the argument to economies that produce many consumption goods, as

in the famous paper by Dornbusch et al. (1977), is rather straightforward. Since our pur-

pose is to show that the (negative) result of the subsection 4.1 still holds, it is enough to

assume that the production of all consumption goods 𝑧 requires labour and the same cap-

ital good, commodity 121. On this basis, condition [16] still determines the normal price

of the generic commodity 𝑧 in country 𝑖 and condition [25] still ensures that the capital

good can be profitably produced only in country B. Therefore, exclusion from trade of

country A can be assessed by means of a generalized version of [21], which must now

hold for every possible𝑧. This is:

𝑇(𝑧, 𝑟) < 0, ∀𝑧 [21’]

In appendix B we provide a numerical example of this case.

Clearly, while with many consumption goods complete exclusion from trade may not

be empirically relevant for most countries, what this theoretical possibility does suggest

is that policies that attempt to promote national competitiveness of some sectors by

prompting a fall in real wages, may not be successful if the country only has at its disposal

backward methods of production that employ imported means of production. We will

return to this point in the conclusions of the article.

4.3. Trade-exclusion with no factor mobility

We conclude this section by showing why even under the presence of capital goods in

production, exclusion from trade is impossible when both labour and capital are immobile

across countries, provided that both distributive variables – wages and profit rates – are

flexible enough.

Consider a hypothetical situation in which country A is excluded from trade and focus

first on the conditions of production of the capital good. Specifically, let us examine the

possible distributive configurations that would allow country A to overcome country B in

the production of this commodity. This would happen if 𝑐1𝐴 = 𝑝1 (with 𝑝1 = 𝑐1

𝐵 because

country B is producing both goods). In other words, [18] must hold:

𝑐1𝐴 =

(1 + 𝑟)𝑙1𝐴

1 − 𝑎11𝐴 (1 + 𝑟)

𝑤𝐴 = 𝑝1 [18]

However, if the profit rate was higher than the maximum profit rate in country A (con-

dition [25] held), the production of the capital good was precluded in country A because

the capital-good sector would earn the same profit rate as in country B only under a neg-

ative wage in country A. In other words: if 𝑟 > 𝑅𝐴, then 1 < 𝑎11𝐴 (1 + 𝑟) and therefore

𝑐1𝐴 = 𝑝1 would require 𝑤𝐴 < 0 (see also [26]).

21 The assumption that all commodities are produced with the same capital good is of course highly

restrictive. But since our purpose here is negative, it is enough to consider this case. If any, the allowance

for more capital goods would strengthen our conclusions.

17

On the contrary, with the full immobility of capital, the constraint imposed by [25]

vanishes. Therefore, if, for the sake of argument, both distributive variables in country A

are free to adjust, it is to be expected that 𝑟𝐴 falls, if necessary 22, below 𝑅𝐴. Then: 1 >

𝑎11𝐴 (1 + 𝑟𝐴) will eventually hold; from [18], it follows that there are non-negative com-

binations (𝑟𝐴,𝑤𝐴) that allow country A not to be excluded in the production of the capital

good. Then, due to the assumed flexibility in distributive variables, one of these pairs will

be achieved23.

Although the previous argument is enough to avoid complete exclusion from trade, it

is worth making some remarks about the consumption-goods industries. The first thing to

be noticed is that the fall in distributive variables in country A could allow some of the

consumptions goods to reach competitiveness before the capital good does. The price of

the generic consumption good 𝑧 would be given by 𝑐𝑧𝐴 = (1 + 𝑟𝐴)(𝑙𝑧

𝐴𝑤𝐴 + 𝑎1𝑧𝐴 𝑐1

𝐵) and,

since the capital good is being produced in country B, in this case it is not even necessary

that 𝑟𝐴 < 𝑅𝐴.

At any rate, as it was the case with capital as anticipated wages, there is always a

distributive configuration that allows every industry 𝑧 to reach competitiveness. This is

because, with appropriate reductions in distributive variables, the capital good will be

eventually produced in country A and therefore, the cost of production of any consump-

tion good could be arbitrarily reduced. In fact, with the capital good being domestically

produced, the cost of production of every commodity 𝑧 is determined by:

𝑐𝑧𝐴 = (1 + 𝑟𝐴) (𝑙𝑧

𝐴 +(1 + 𝑟𝐴)𝑎1𝑧

𝐴 𝑙1𝐴

1 − 𝑎11𝐴 (1 + 𝑟𝐴)

)𝑤𝐴 [27]

which clearly tends to zero if both 𝑟𝐴 and 𝑤𝐴 are arbitrarily reduced, and therefore com-

petitors in country B can be eventually overcome.

5. Conclusions

Within standard Ricardian models of trade, real wage flexibility ensures the possibility of

specialization (every country has absolute advantage in the production of some good).

We have shown, however, that this result crucially depends on the possibility that com-

modities are produced by unassisted labour alone. Or, when the presence of capital goods

is admitted in production (and it should!), on the further – increasingly implausible, in the

current era of globalization – assumption that not only labour, but especially capital, are

completely immobile across countries. Although, in some way or another, either of the

two assumptions was always present in the literature since David Ricardo (1951), any

attempt to remove them, at least partially, as would be the case with the simple acceptance

of production of capital goods with a limited mobility of capital, overturns conclusions

22 If necessary because, as it is discussed in the following paragraph, it could be the case that some con-

sumption good industries become competitive before the capital good does and it is not required that 𝑟𝐴

keeps falling below 𝑅𝐴 to prevent exclusion. 23 Which particular distributive configuration will be reached cannot be determined a priori, and is beyond

the scope of the present article.

18

of traditional Ricardian models that have become sort of ‘common knowledge’ for inter-

national trade theorists.

Our theoretical results show why, contrarily to what is often heard in both mainstream

and heterodox academic circles, but also in the political arena, the adjustment mechanism

in income distribution that should re-establish trade imbalances, or problems of financing

in foreign currency, through its impact on the competitiveness of domestic production,

cannot be accepted. For we have shown that when capital mobility is duly considered,

competitiveness of domestic production may not be achieved for any distributive config-

uration that (reasonably) excludes negative values. It explains why in these peripheral

economies the fall in real wages may be able to correct external deficits only by means of

its impact on aggregate income, that precisely induces a decrease in the level of imports

of capital goods. These results are in line with the numerous empirical studies that support

the conclusions of the so-called ‘elasticity pessimism’.

Now, while complete trade exclusion may be considered as an implausible result, our

argument can also be interpreted in terms of sectorial, rather than national, competitive-

ness. Consider for example those (many) countries that only manage to produce and, fun-

damentally, export, goods within a single industry, usually natural-resource based.

Among trade theorists, it would be ‘natural’ to conclude that, had these countries not been

endowed with abundant natural resources (had not suffered, the so-called ‘curse of natural

resources’), they would have managed to produce some other commodity, anyway. “A

country must always possess a comparative advantage in something” (Clarida and

Findlay, 1991, p. 31, our italics), it is, indeed, often argued. On the contrary, our argument

has shown that technological backwardness may imply that, besides these primary goods,

other ‘somethings’ need not exist.

In fact, the argument developed in the paper has shown that, from a sectorial perspec-

tive, international competitiveness may be hindered by the inefficiency in the employment

of capital goods (in the model considered in the article, depicted by the consumption-

goods sector) or, alternatively, in the production of the capital goods themselves. On the

one hand, we have argued that exclusion due to the former lays in the presence of im-

ported inputs, since these set a positive lower bound to production costs, which, moreo-

ver, rise with the backwardness of the sector. Furthermore, if, for the sake of argument,

one disregarded the reasons behind the presence of these imported inputs, this positive

lower bound would exist even if the assumption of free capital mobility across countries

were dropped. On the other hand, the moment that at least some capital mobility across

countries is admitted, we have shown that exclusion in the production of capital goods

arises when the level of the international profit rate is higher than the maximum level

affordable by the domestic production of these goods. The validity of this condition may

seem, at first glance, too restrictive – or even ad hoc – to hold in reality. On closer in-

spection, however, it is not. This could be more easily grasped if one considers its limiting

case – that would appear almost evident for many developmentalist scholars – in which

no method of production for the capital goods is available at all, as witnessed in many

peripheral economies. Under these conditions, the domestic production of these goods

would not be possible even at a zero profit rate. An interesting implication of this rather

19

limiting, but still plausible, situation, is that the mobility of capital across countries is not

even a necessary assumption for the results of the paper to hold.

The consequences of all this can hardly be underestimated. They strongly suggest that

different strategies, which much more actively involve the participation of the State than

simply ‘putting the prices right’, should be taken both to embark backward economies

into a process of sustained growth or to induce structural change.

Appendix A: Exclusion from trade under full wage flexibility, the two-commodities

case

The present appendix gives a numeral example that shows that exclusion from trade is

possible under full wage flexibility when production requires the employment of a capital

good and capital is mobile across countries. The available production methods are shown

in Table A1.

Country A Country B

𝑧 0 1 0 1

𝑎1𝑧𝑖 5/3 4/5 1 ½

𝑙𝑧𝑖 1 1 2 1

Table A1- Available production methods

The maximum profit rate affordable by the capital-good sector in each country is:

𝑅1𝐴 = 25%𝑅1

𝐵 = 100% [A1]

Assume the global profit rate is 𝑟 = 50%. Therefore, the capital good can only be pro-

duced in country B, regardless the wage rate.

If the capital good is taken as the numeraire (𝑝1 = 1), we have that:

1 = 𝑐1𝐵 =

(1 + 𝑟)𝑤𝐵𝑙1𝐵

1 − 𝑎11𝐵 (1 + 𝑟)

= 6𝑤𝐵 [A2]

and hence:

𝑤𝐵 =1

6 [A3]

We can now proceed to examine the conditions of production of commodity 0. We

determine first, the cost of production of this commodity in country B,

𝑐0𝐵 = (1 + 𝑟)(𝑎10

𝐵 𝑝1 + 𝑤𝐵𝑙𝑜𝐵) = 2 [A4]

next, we determine the cost of production in country A, under a zero-wage rate:

𝑐𝑜𝐴 = (1 + 𝑟)𝑎10

𝐴 𝑝1 = 2.5 > 2 = 𝑐𝑜𝐵 [A5]

20

The conclusion is that country A cannot profitably produce neither commodity 0 nor com-

modity 1, even after 𝑤𝐴 has dropped to zero. Therefore, A is excluded from trade24.

Appendix B: Exclusion with many consumption goods

The present appendix shows that exclusion from trade is still possible if there are many –

actually an infinite number of – consumption goods; that is, the generic consumption good

𝑧 is indexed within the interval [0; 1) while commodity 1 is the capital good. The availa-

ble production methods are shown in Table B1.

Country A Country B

𝑧 𝑧(with𝑧 ≠ 1) 1 𝑧(with𝑧 ≠ 1) 1

𝑎1𝑧𝑖 5(2 − 𝑧)/3 4/5 2 − 𝑧 ½

𝑙𝑧𝑖 1 1 2 1

Table B1- Available production methods

Note that the methods of production available in the capital-goods industries are the

same as those presented in table A1. Therefore, as before, the maximum profit rates af-

fordable by each of these sectors are the ones presented in condition [A1]. If we still

assume that 𝑟 = 50%, the capital good will be produced in country B alone.

Now, we can examine the conditions of production of the remaining z (with 𝑧 ≠ 1)

commodities. To that end, we determine first, the cost of production of these commodities

in country B:

𝑐𝑧𝐵 = (1 + 𝑟)(𝑎1𝑧

𝐵 𝑝1 +𝑤𝐵𝑙𝑧𝐵) =

2 − 9𝑧

6 [B1]

Next, we can proceed to calculate these costs in country A:

𝑐𝑜𝐴 = (1 + 𝑟)(𝑎1𝑧

𝐴 𝑝1 + 𝑤𝐴𝑙𝑧𝐴) =

27 + 9𝑧 + 𝑤𝐴

6 [B2]

Note that 𝑐𝑜𝐴 > 𝑐𝑜

𝐵 even if 𝑤𝐴 = 0. In this latter case we would have:

𝑐𝑜𝐴 − 𝑐𝑜

𝐵 = 2.5 + 3𝑧 > 0∀𝑧 ∈ [0; 1) [B3]

Therefore, country A cannot profitably produce any commodity even when its rate of

wages arbitrarily decreases, with the implication that it will be excluded from trade.

It may be finally useful to construct our 𝑇(𝑧; 0.5) function for this case, as is shown in

the graph below.

24 Note that in this case, condition [24] from the text holds, since: (𝑎10

𝐴 − 𝑎10𝐵 )𝑝1 = 2/3 > 1/3 = 𝑤𝐵𝑙0

𝐵

21

Figure B1- Exclusion from trade in the continuum-of-goods case

The graph shows that the maximum relative wage 𝜔 required for any of the infinite

number of consumption goods to be produced less costly in country A than in country B,

is negative, with the implication that for any (economically meaningful) level of the wage

rate in country A, this country will be excluded from trade.

0.2 0.4 0.6 0.8 1.0z

30

20

10

22

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24

Authors contact information:

Eduardo Crespo

Institute of Economics, Federal University of Rio de Janeiro.

21941-972 Rio de Janeiro - (Brazil)

ecres70@gmail.com

Ariel Dvoskin

CONICET - IDAES National University of San Martín.

B 1650 Buenos Aires - (Argentina)

advoskin@unsam.edu.ar

Guido Ianni

Department of Economics, Roma Tre University.

00145 Rome - (Italy)

guido_ianni@yahoo.com